Perovskite solar cells have emerged as a promising technology for next-generation photovoltaics due to their high power conversion efficiencies, low-cost fabrication, and tunable optoelectronic properties. Among various perovskite materials, formamidinium lead iodide (FAPbI3) has attracted significant attention because of its near-ideal bandgap of approximately 1.47 eV, which is close to the Shockley-Queisser limit, and its excellent charge carrier mobility. However, the practical application of FAPbI3-based perovskite solar cells is hindered by the inherent thermodynamic instability of its photoactive cubic black phase (α-phase). This phase tends to transform into a non-perovskite yellow phase (δ-phase) under ambient conditions, leading to rapid degradation of device performance. The instability primarily stems from the large ionic radius of the formamidinium cation (FA+), which induces lattice strain and distortions in the [PbI6]4− octahedral framework.
To address these challenges, compositional engineering via cation substitution has been widely explored. In particular, cesium (Cs) doping has been shown to enhance the phase stability of FAPbI3 without compromising its optoelectronic properties. Cesium is an alkali metal with a smaller ionic radius compared to FA+, and its incorporation into the perovskite lattice can reduce lattice strain and suppress phase segregation. Moreover, cesium is an abundant resource in salt lakes, and its utilization in high-value applications like perovskite solar cells could promote the sustainable development of cesium-based industries. While previous studies have focused on polycrystalline films, the presence of grain boundaries and defects in such systems often masks the intrinsic effects of Cs doping. Therefore, single-crystal studies are essential to elucidate the fundamental mechanisms behind stability enhancement.
In this work, we systematically investigate the impact of Cs solid solution on the stability and optoelectronic properties of FAPbI3 single crystals. We synthesized a series of (FAxCs1−x)PbI3 single crystals with varying Cs concentrations (x = 0, 0.05, 0.1, 0.15) and constructed their dissolution equilibrium phase diagram. The crystals were characterized using X-ray diffraction (XRD), photoluminescence (PL) spectroscopy, time-resolved photoluminescence (TRPL), and density functional theory (DFT) calculations. Our results reveal that Cs doping significantly improves the phase stability of FAPbI3, with optimal performance achieved at 10% Cs concentration. The enhanced stability is attributed to reduced defect density, improved lattice uniformity, and modified electronic structure. These findings provide valuable insights for the development of stable and efficient perovskite solar cells and highlight the potential of cesium resources in advanced energy applications.
The synthesis of (FAxCs1−x)PbI3 single crystals was carried out using a controlled temperature gradient method. Precursor solutions with different molar ratios of FAI, CsI, and PbI2 were prepared in γ-butyrolactone (GBL) solvent. The solutions were heated gradually to induce nucleation and crystal growth. To obtain large-sized single crystals, seed crystals were selected and immersed in the precursor solution for secondary growth. The crystals were then purified through multiple washing steps and dried under vacuum. The detailed synthesis conditions are summarized in Table 1.
| Cs Concentration (x) | Precursor Concentration (mol/L) | Temperature Range (°C) | Growth Time (h) |
|---|---|---|---|
| 0 | 1.6 | 90-150 | 24 |
| 0.05 | 1.4 | 90-150 | 24 |
| 0.10 | 1.2 | 90-150 | 24 |
| 0.15 | 1.1 | 90-150 | 24 |
The dissolution equilibrium phase diagram for the (FAxCs1−x)PbI3 system was established to guide the crystal growth process. As shown in Figure 1, the phase diagram is divided into four distinct regions: Region I corresponds to the liquid phase of the precursor solution; Region II is the solid-liquid coexistence region where δ-CsPbI3 precipitates as yellow needle-like crystals; Region III is a three-phase region where α-(FAxCs1−x)PbI3, δ-CsPbI3, and liquid coexist; and Region IV is the target phase region where only α-(FAxCs1−x)PbI3 crystals are stable. For Cs concentrations below 8%, simply increasing the temperature allows the system to enter Region IV directly, enabling the growth of phase-pure α-phase single crystals. However, for Cs concentrations between 8% and 15%, the system must pass through Region II quickly to avoid the formation of δ-CsPbI3 impurities. This is achieved by rapid heating to reach the inverse temperature solubility curve of (FAxCs1−x)PbI3. Above 15% Cs concentration, the solvent boiling point limits further doping, indicating that 15% is the solid solution limit under these conditions.
X-ray diffraction (XRD) analysis was performed to examine the crystal structure and phase purity of the synthesized single crystals. The XRD patterns for different Cs concentrations are shown in Figure 2. All samples exhibit strong diffraction peaks at 14.2° (100), 28.1° (200), and 31.5° (210), corresponding to the cubic perovskite structure. No peak splitting is observed, indicating high crystallinity and phase homogeneity. However, for Cs concentrations of 0.05, 0.10, and 0.15, weak peaks appear at 19.9° (110), 24.1° (111), and 31.5° (211), which are attributed to the δ-phase. The intensity of these peaks increases with higher Cs content, suggesting that excessive doping promotes the formation of the non-perovskite phase. Additionally, the (200) diffraction peak shifts to higher angles with increasing Cs concentration, indicating lattice contraction due to the smaller ionic radius of Cs+ compared to FA+. The lattice parameters were calculated using Bragg’s law:
$$n\lambda = 2d\sin\theta$$
where λ is the X-ray wavelength, d is the interplanar spacing, and θ is the diffraction angle. The lattice constant a for the cubic structure is related to d by:
$$a = d\sqrt{h^2 + k^2 + l^2}$$
The calculated lattice parameters are summarized in Table 2.
| Cs Concentration (x) | Lattice Constant a (Å) | PL Peak (nm) | Bandgap (eV) | TRPL Lifetime (μs) |
|---|---|---|---|---|
| 0 | 6.35 | 836 | 1.48 | 2.1 |
| 0.05 | 6.32 | 820 | 1.51 | 5.4 |
| 0.10 | 6.30 | 797 | 1.56 | 4.8 |
| 0.15 | 6.28 | 785 | 1.58 | 3.5 |
Photoluminescence (PL) spectroscopy was used to study the optical properties of the single crystals. The PL spectra for different Cs concentrations are shown in Figure 3. As the Cs content increases, the PL peak shifts from 836 nm for pure FAPbI3 to 797 nm for (FA0.85Cs0.15)PbI3, indicating a blue shift of 39 nm. This corresponds to an increase in the optical bandgap from 1.48 eV to 1.58 eV. The bandgap widening can be attributed to the lattice contraction and changes in the electronic structure induced by Cs doping. The bandgap energy Eg is related to the PL peak wavelength λ by:
$$E_g = \frac{1240}{\lambda}$$
where Eg is in eV and λ is in nm. The observed bandgap tuning is beneficial for tandem perovskite solar cell applications, where wider bandgaps are required for efficient photon harvesting.
Time-resolved photoluminescence (TRPL) measurements were conducted to investigate the carrier dynamics in the single crystals. The TRPL decay curves are shown in Figure 4. All curves exhibit bi-exponential decay behavior, which can be fitted using the equation:
$$I(t) = A_1 e^{-t/\tau_1} + A_2 e^{-t/\tau_2}$$
where I(t) is the PL intensity at time t, A1 and A2 are amplitudes, and τ1 and τ2 are decay time constants. The average lifetime τavg is calculated as:
$$\tau_{avg} = \frac{A_1 \tau_1^2 + A_2 \tau_2^2}{A_1 \tau_1 + A_2 \tau_2}$$
The calculated lifetimes are listed in Table 2. Pure FAPbI3 has a short lifetime of 2.1 μs, which increases to 5.4 μs for 5% Cs doping. This enhancement is due to reduced defect density and suppressed non-radiative recombination. However, at higher Cs concentrations (10% and 15%), the lifetime decreases slightly, likely due to increased lattice strain and the formation of new recombination centers. The optimal carrier lifetime at 5% Cs doping suggests that moderate Cs incorporation improves charge carrier mobility, which is crucial for high-performance perovskite solar cells.
Density functional theory (DFT) calculations were performed to gain insights into the electronic structure and stability of Cs-doped FAPbI3. The crystal structures of (FAxCs1−x)PbI3 for x = 0, 0.05, 0.10, and 0.15 were modeled, and the density of states (DOS) was computed. The DOS plots are shown in Figure 5. For pure FAPbI3, the valence band maximum (VBM) is dominated by I-5p orbitals, while the conduction band minimum (CBM) consists of Pb-6p orbitals. With Cs doping, the Cs-5p orbitals contribute to the conduction band, leading to an upward shift of the CBM and a widening of the bandgap. This is consistent with the PL results. The Gibbs free energy ΔG for the phase transition from α-phase to δ-phase was calculated using:
$$\Delta G = \Delta E + \Delta E_{ZPE} – T\Delta S$$
where ΔE is the electronic energy difference, ΔEZPE is the zero-point energy change, T is temperature, and ΔS is the entropy change. The results show that ΔG becomes more negative with increasing Cs content, indicating enhanced phase stability. The step-terrace diagram in Figure 6 illustrates the energy landscape, confirming that 10% Cs doping yields the lowest Gibbs free energy, corresponding to the highest thermodynamic stability.
The stability of the single crystals was evaluated under harsh environmental conditions, including exposure to moisture (43% relative humidity) and continuous illumination under AM1.5G solar simulator. The XRD patterns after aging are shown in Figures 7 and 8. Pure FAPbI3 undergoes complete phase transformation to the δ-phase after 1000 hours, while Cs-doped samples retain the α-phase even after 2000 hours. In particular, (FA0.90Cs0.10)PbI3 shows no detectable δ-phase peaks, demonstrating superior stability. This enhancement is attributed to the reduced defect density, improved lattice uniformity, and stronger Pb-I-Cs bonding interactions. The stability data are summarized in Table 3.
| Cs Concentration (x) | Time to δ-phase Formation (h, humidity) | Time to δ-phase Formation (h, illumination) | Phase Purity After 2000 h |
|---|---|---|---|
| 0 | 1000 | 800 | Degraded |
| 0.05 | >2000 | >2000 | Stable |
| 0.10 | >2000 | >2000 | Stable |
| 0.15 | 1800 | 1600 | Partial degradation |
In conclusion, our study demonstrates that cesium solid solution significantly enhances the stability and optoelectronic properties of formamidinium lead iodide perovskite single crystals. The dissolution equilibrium phase diagram provides a roadmap for growing high-quality single crystals with controlled Cs concentrations. Cs doping widens the bandgap, reduces defect density, and improves carrier lifetime, with optimal performance achieved at 5-10% Cs content. DFT calculations reveal that the stability enhancement is due to favorable changes in the electronic structure and Gibbs free energy. The improved stability under humidity and illumination makes Cs-doped FAPbI3 a promising material for durable perovskite solar cells. These findings not only advance the fundamental understanding of perovskite stability but also highlight the potential of cesium resources in renewable energy technologies. Future work will focus on integrating these single crystals into efficient and stable perovskite solar cell devices.
The development of stable perovskite solar cells is crucial for the commercialization of perovskite-based photovoltaics. The insights gained from this study on Cs-doped FAPbI3 single crystals can be extended to other perovskite compositions and device architectures. For instance, the bandgap tuning achieved through Cs doping could be exploited in tandem solar cells, where perovskite solar cells are combined with silicon or other semiconductors to achieve higher efficiencies. Additionally, the use of cesium from salt lake resources aligns with the goals of sustainable and eco-friendly material sourcing. Further research should explore the long-term stability under operational conditions and the scalability of single-crystal growth for large-area perovskite solar cell applications.
In summary, we have systematically investigated the effect of cesium solid solution on the stability of formamidinium lead iodide perovskites. Our results show that Cs doping effectively suppresses the phase transition from α-phase to δ-phase, improves optoelectronic properties, and extends the lifetime of the material. These advancements contribute to the ongoing efforts to develop reliable and high-performance perovskite solar cells for the global energy market.